Determining Expectancy in Your Trading

Posted on August 12, 2008 by John Jagerson

Traders need to have a solid and realistic understanding of what they expect in the future, and specifically what returns they expect to produce in terms of profits. I ask traders all the time what kind of returns or draw-downs they are expecting in their account and a surprising number say they have no idea or give me their goals rather than planned long term returns. They want to be profitable, but don’t understand how a string of trades may impact overall portfolio value. This kind of trading without planned expectations and rules is a major barrier to success.

So what’s the problem with not knowing what to expect?

Random Trading

Many traders have a propensity for random trading. These kinds of traders seem to be fishing for opportunities. They may take a trade or two from someone else they saw on a forum or newsletter, or they may just be entering trades without a firm risk control procedures in place. They have a tendency to “wait and see what happens.” Usually, what happens is a gut wrenching period of indecision, loss and frustration.

Misunderstanding of trading costs

The second issue these traders deal with is a lack of understanding of system or strategy costs. I usually refer to this as “trader myopia” or “tunnel vision.” These traders concentrate on one trade at a time and are not thinking about tomorrow, or next month’s trades, and don’t understand the costs that can impact results in the long term.

In this section we will address those issues, and walk through the process of developing accurate expectancy for a trading strategy.

What is expectancy?

Expectancy is what it sounds like. It helps you understand how winners, losers, gains and losses relate to each other over the long term. This process helps you understand what your trading system profits should be, and helps validate your backtesting.

In this lesson, we will develop expectancy in three steps. First, you will calculate your win- and loss-ratios. Second, you will calculate your reward-to-risk ratio. Finally, you will combine the two numbers into an expectancy ratio. That information will help to understand what you can expect in the future.

Steps for developing expectancy

Win and loss ratios

This is a simple number to calculate. First, from your back-testing period, sum the total number of trades that would have been taken. Next, total the number of winning trades from that set. Finally, divide the number of winning trades by the total number of trades. This gives you your win ratio. Imagine that you have a strategy that you have tested over 150 total trades with a win ratio of 28%. That means the system results in a profitable trade 28% of the time and losers 72% of the time. The win and loss ratios are calculated like this:

(42 Total winners) / (150 Total trades) = 28% win ratio

100% – (28% win ratio) = 72% loss ratio

This may seem very low, but as we continue we see that doesn’t mean the system isn’t profitable.

Reward to risk ratio

This is also a relatively simple number to calculate. The risk to reward ratio therefore, is simply the average size of a profitable trade divided by the average size of a losing trade. Imagine that in your trading strategy your winners are 5 times larger than your losers. That will make your reward to risk ratio 5.

($500 Winner size) / ($100 Loser size) = 5

Expectancy ratio

At this point we can combine these two numbers to create an expectancy ratio. This is a simple process of multiplying the reward to risk ratio (5) by the percentage of winning trades (28%), and subtracting the percentage of losing trades (72%), which is calculated like this:

(Reward to Risk ratio x win ratio) – Loss ratio = Expectancy Ratio

(5*28%) – (72%) = .68

Superficially, this means that on average you expect this strategy’s trades to return .68 times the size of your losers. This is important for two reasons: First, it may seem obvious, but you know right away that you have a positive return. Second, you now have a number you can compare to other candidate systems to make decisions about which ones you employ.

It is important to remember that any system with an expectancy greater than 0 is profitable using past data. The key is finding one that will be profitable in the future.

You can also use this number to evaluate the effectiveness of modifications to this system.

Other Factors

Expectancy is an important factor but there are three fundamental considerations that are important to note when developing it:

1. Trading costs There is a simple method to help better understand the affects of trading costs on your system. Reduce the gains in your winners by the amount of trading costs, and increase your losers similarly. As I mentioned in a previous section, it is also good to assume a certain amount of slippage during entry. In other words, never assume that things will work out perfectly in your trades.

2. Position SizingFrom here you need to begin working on understanding how expectancy works with position sizing. An expectancy ratio may look good, but without proper and consistent position sizing (use of leverage, margin and lot size), your actual performance could still be poor. We will talk about position sizing in more detail again.

3. Historical versus Future ResultsIt is important to point out that when you are building and testing a system initially, you rely on very fallible data. Past data is certainly useful, and it is the best alternative when you are developing an idea. However, the past is NOT an indication of what WILL happen in the future. You will not likely see results perfectly consistent with what you saw in the past over your testing period. It just doesn’t happen.

Rather than invalidating your expectancy analysis, however, I think this makes it even more important.

Summary

Expectancy is a great way to compare and analyze strategies and strategy modifications. It is a solid double-check on the viability of the strategy itself. If your expectancy ratio is negative you should not trade the strategy.

Expectancy also serves an important planning purpose. I always compare developing an expectancy ratio to the pre-flight checklist that a pilot uses before take off. If you are able to answer all the questions required for an expectancy ratio then you have done some good planning. If one of your trading factors is blank, or only an estimate, you need to solidify it before executing on your system.

Disclosures

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